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I'm thinking of building a 1 or 2 foot bed right up against my house, using the house as one side of the bed. We have a brick exterior and it really heats up. I'm thinking it might be a good cold frame in the winter.Are there any issues with putting the bed up against the house?

I hate to be the one naysayer, but if you live in an area with termites (which is pretty much anywhere in the US) or carpenter ants, having soil that high up and close to the house siding could significantly increase the potential for an infestation. Couple that with the fact that the typical treatments you would not want around a vegetable garden, and it makes it a risk. Generally you want at least 10-12 inches of exposed foundation clear above the soil level to the house sheathing.

It looks beautiful, but at the very least I suggest being on the lookout and inspecting for ant or termite trails on the foundation frequently.

You need to make sure your house was never treated for termites. We had ours treated 12 years ago and the company told us flower beds against the house were fine, but that we could never plant edibles alongside the house for at least 8 feet. They drilled holes in the slab and along the outside, brick walls to insert the insecticide and they said it would leech into the soil. We were told to just consider that 8 foot strip alongside the house a "dead zone" as far as planting any edibles - including fruit trees - for the duration of time.

The usual square foot gardening idea is you don't use your own soil anyway. If you raise the bottom of your beds a little above the soil, and then use Mel's Mix, it shouldn't make any difference what's in the soil unless there's some tremendous off-gassing from it.

If you make your beds out of something besides wood, that would take the termite worries out of things too. I was just at a neighbor's house today. His garden is made out of cinder blocks. And I've seen beautiful brick planters before. Stone or brick would probably look great close by your brick house.